Non-stationary Polarization: Proof and Application
Yizhi Zhao, Lingjuan Wu, Shiwei Xu, Yuling Fan · arXiv (Cornell University) · 2018
In this paper we consider the polarization theory of non-stationary channels and its application in secure coding. For non-stationary polarization, we construct a multi-channel stochastic process by which we extend Arikan's standard methods and prove that the sequence of non-stationary channels can be polarized the into full noise channels and noiseless channels by the channel polarization transformation. Then for non-stationary wiretap channel model, we construct a secure polar coding scheme by applying the non-stationary polarization. Theoretically, we prove that this secure coding scheme achieves the average secrecy capacity of the non-stationary WTC model under both reliability and strong security criterions. Moreover, we carry out simulations to test the performance of proposed scheme, and the testing results also prove the achieving of reliably and security.